Question

According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the ________________. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent. Therefore, one can say that segment ER is congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The Side-Angle-Side (SAS) Theorem says triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.

Answer 1

Unfortunately, this problem apparently comes without a diagram (or you have not shared the diagram that came with it).  I'd strongly suggest either finding and posting the diagram or sketching your own diagram.  Then we could refer to the rectangle more meaningfully (more specifically).  Next, please identify what it is that you need to know to get started.

To be frank, your post looks like an explanation of a rectangle problem;  you don't appear to be asking a question except for the one place where there's a blank that you're supposed to fill in.